50x^2=75

Solution for 50x^2=75 equation:

50x^2=75

We move all terms to the left:

50x^2-(75)=0

a = 50; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·50·(-75)
Δ = 15000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15000}=\sqrt{2500*6}=\sqrt{2500}*\sqrt{6}=50\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{6}}{2*50}=\frac{0-50\sqrt{6}}{100}
=-\frac{50\sqrt{6}}{100}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{6}}{2*50}=\frac{0+50\sqrt{6}}{100}
=\frac{50\sqrt{6}}{100}
=\frac{\sqrt{6}}{2}
$